Construction method of non-continuous structural plane shear constitutive model

Abstract

The application discloses a construction method of a non-continuous structural surface shearing constitutive model, which comprises the following steps: obtaining peak value and residual stage shearing strength parameters; obtaining initial rock mass shearing strength τ of the non-continuous structural surface based on Jennings criterion; introducing coefficient ξ j and ξ r respectively to adjust normal stress at joints and rock bridges, and introducing coefficient ω to adjust cohesion in the rock bridges to obtain adjusted rock mass shearing strength τ of the non-continuous structural surface; obtaining three non-continuous structural surface failure criteria of tension, shearing and strength failure based on Lajtai rock bridge failure theory criterion; and obtaining corresponding non-continuous structural surface shearing constitutive models under tension failure conditions, shearing failure conditions and strength failure conditions of the rock bridges. The non-continuous structural surface shearing constitutive model can effectively describe the shearing behavior characteristics of the non-continuous structural surface and effectively improve the practicability of the constitutive model.

Description

Technical Field

[0001] This invention relates to the field of constitutive models of rock structural surfaces, and in particular to a method for constructing a shear constitutive model of discontinuous structural surfaces. Background Technology

[0002] In modern geotechnical engineering, rock bolts are one of the important support methods to ensure the long-term stability and safety of engineering rock masses. Since the 1980s, numerous experts and scholars at home and abroad have focused on the fact that rock bolts not only fix loose rock blocks to stable rock layers in the axial direction, but also enhance the shear slip of joint surfaces in the lateral direction. However, in rock mass systems with rock bolts, the interaction between rock bolts, rock blocks, and joints is complex and unclear. In addition, weak structural surfaces within the rock mass usually retain a certain strength and cannot be simply regarded as open joints or faults. In particular, engineering rock masses are often affected by multiple sets of joints, which further increases the complexity of rock mass failure and the difficulty of support control.

[0003] like Figure 1 As shown, under shear stress, cracking and propagation failure first occur at the rock bridge within the discontinuous joint. The anchor bolts bend after the rock blocks slide and shift, providing shear, tensile, or compressive forces near the joint surfaces they pass through. This negative feedback effect prevents the rock blocks from shearing and sliding against the rock bridge. Therefore, it is necessary to further understand the mechanical properties of the discontinuous rock mass during this process. However, problems exist, such as unclear physical and mechanical meanings of the parameters and insufficient description of important displacement field evolution laws. In constitutive model research, the clarity of the physical and mechanical meanings of the model parameters is a crucial factor determining the model's value for engineering applications. Summary of the Invention

[0004] Based on this, the purpose of this invention is to provide a method for constructing a shear constitutive model of a discontinuous structural surface, which can effectively describe the shear behavior characteristics of the discontinuous structural surface and effectively improve the practicality of the constitutive model.

[0005] To solve the above-mentioned technical problems, the present invention adopts the following technical solution:

[0006] This invention provides a method for constructing a shear constitutive model of a discontinuous structural surface, which includes the following steps:

[0007] Step S1: Using different normal stresses σ n Peak intensity τ in the shear stress-strain curve of a discontinuous structural surface at shear failure p and residual strength τ r By fitting the data separately and applying the Mohr-Coulomb criterion, the peak and residual stage shear strength parameters can be obtained: cohesion c and internal friction angle.

[0008] Step S2: Obtain the initial rock mass shear strength τ of the discontinuous structural plane based on the Jennings criterion;

[0009] Step S3: Introduce the coefficient ξ j and ξ r The normal stress at joints and rock bridges is adjusted separately, and the cohesion of the rock bridge is adjusted by introducing a coefficient ω. The shear strength τ of the rock mass at the discontinuous structural surface after adjustment is obtained.

[0010] Step S4: Obtain failure criteria for three discontinuous structural planes—tension, shear, and strength failure—based on the Lajtai rock bridge failure theory criteria;

[0011] Step S5: Obtain the shear constitutive models of the discontinuous structural surfaces corresponding to the tensile failure, shear failure, and strength failure conditions of the rock bridge.

[0012] In one embodiment, step S2 includes:

[0013] Based on the Mohr-Coulomb strength criterion, the shear stress of a discontinuous structural plane is composed of both joint surfaces and rock bridges. That is, the shear strength τ of the rock mass at a discontinuous structural plane is determined by the shear coefficients of the joint surfaces and rock bridges, the cohesion c, and the internal friction angle. Combined with weighted calculation using connectivity k as the coefficient to obtain

[0014]

[0015] in, c is the overall equivalent shear strength coefficient of the structural surface; j , c is the shear coefficient of the joints in the structural plane; r , is the shear resistance coefficient of the rock bridge in the structural plane.

[0016] In one embodiment, the rock mass shear strength of the discontinuous structural plane in step S3 satisfies

[0017]

[0018] Wherein, the coefficient ξ j Both ω and ξ take values ​​between 0 and 1, and the coefficient ξ j and ξ r The relationship between the connectivity k between the joints and the joints is as follows:

[0019]

[0020] In one embodiment, the specific steps of step S4 are as follows:

[0021] Based on the Lajtai rock bridge failure theory criteria, failure criteria for three types of discontinuous structural planes—tension, shear, and strength failure—are derived. The shear strength τ of the rock mass at the discontinuous structural plane is expressed piecewise according to the magnitude of the normal stress, satisfying the following formulas sequentially.

[0022] Criteria for determining tension failure:

[0023]

[0024] Shear failure criterion:

[0025]

[0026] Strength failure criterion:

[0027]

[0028] Where: C is the joint surface adjustment parameter, ranging from 0 to 1; σ t The tensile strength of intact rock, MPa; c r The cohesive force within intact rock, MPa; The internal friction angle of intact rock, in °. The internal friction angle of the intact rock is °.

[0029] In one embodiment, step S5 includes:

[0030] Mechanical analysis was performed at different locations on the rock bridge to obtain the normal stress σ of the micro-element. a and tangential stress τ a :

[0031]

[0032] Where, τ j Characterized as the shear strength of the joint itself;

[0033] Obtain the normal stress σ of the plane at an angle β to the horizontal direction. β and tangential stress τ β :

[0034]

[0035] The normal stress (σ) of the plane β Differentiate with respect to angle β, i.e.:

[0036]

[0037] Substituting equation 3-15 into equations 3-13 and 3-14, we can obtain the maximum and minimum stresses σ1 and σ3 on the principal stress plane:

[0038]

[0039] Where, σ x Characterized as horizontally applied stress;

[0040] If the rock bridge experiences initial tensile failure, the minimum principal stress must equal the tensile strength of the rock material, i.e.:

[0041]

[0042] The effective shear stress can be obtained after calculation:

[0043]

[0044] The shear constitutive model of the discontinuous structural surface under the condition of tensile failure of the rock bridge is obtained as follows:

[0045]

[0046] In one embodiment, step S5 includes:

[0047] Mechanical analysis was performed at different locations on the rock bridge to obtain the normal stress σ of the micro-element. a and tangential stress τ a :

[0048]

[0049] τ a =τ s -kτ j (3-12)

[0050] Where, τ j Characterized as the shear strength of the joint itself;

[0051] Obtain the normal stress σ of the plane at an angle β to the horizontal direction. β and tangential stress τ β :

[0052]

[0053] The normal stress (σ) of the plane β Differentiate with respect to angle β, i.e.:

[0054]

[0055] Substituting equation 3-15 into equations 3-13 and 3-14, we can obtain the maximum and minimum stresses σ1 and σ3 on the principal stress plane:

[0056]

[0057] Where, σ x Characterized as horizontally applied stress;

[0058] If the rock bridge experiences initial strength failure, the maximum principal stress must equal the compressive strength of the rock material, i.e.:

[0059]

[0060] The effective shear stress can be obtained after calculation:

[0061]

[0062] The shear constitutive model of the discontinuous structural surface under the condition of strength failure of the rock bridge is obtained as follows:

[0063]

[0064] In one embodiment, step S5 includes:

[0065] Mechanical analysis was performed at different locations on the rock bridge to obtain the normal stress σ of the micro-element. a and tangential stress τ a :

[0066]

[0067] Where, τ j Characterized as the shear strength of the joint itself;

[0068] Obtain the normal stress σ of the plane at an angle β to the horizontal direction. β and tangential stress τ β :

[0069]

[0070] The normal stress (σ) of the plane β Differentiate with respect to angle β, i.e.:

[0071]

[0072] Substituting equation 3-15 into equations 3-13 and 3-14, we can obtain the maximum and minimum stresses σ1 and σ3 on the principal stress plane:

[0073]

[0074] Where, σ x Characterized as horizontally applied stress;

[0075] When the rock bridge experiences shear failure, according to the Coulomb-Navier shear criterion, the effective shear stress... Differentiation

[0076]

[0077] achievable In addition, the shear stress τ on the failure surface β and normal stress σ β By conforming to the Mohr-Coulomb strength criterion and substituting equations 3-8 and 3-9 into equation 3-25, the shear stress of the rock bridge at shear failure can be obtained:

[0078]

[0079] The shear constitutive model of the discontinuous structural surface under the condition of shear failure of the rock bridge is obtained as follows:

[0080]

[0081] In summary, the method for constructing a shear constitutive model of a discontinuous structural surface provided by this invention establishes a shear constitutive model of a discontinuous structural surface, which can effectively describe the shear behavior characteristics of the discontinuous structural surface and effectively improve the practicality of the constitutive model. Attached Figure Description

[0082] Figure 1 The three-dimensional discontinuous structural surface of rock mass in an open landslide provided in the embodiments of the present invention includes (a) a schematic diagram of the failure behavior; and (b) a geological survey of the structural surface after failure.

[0083] Figure 2 A schematic diagram of the failure mechanics analysis of discontinuous structural surfaces and its crack propagation mode provided for embodiments of the present invention;

[0084] Figure 3 Illustration of the failure criteria for the Lajtai rock bridge provided in this embodiment of the invention;

[0085] Figure 4 This invention provides a mechanical analysis of rock mass failure with non-penetrating structural planes, as provided in an embodiment of the invention.

[0086] Figure 5 Comparison of shear stress-strain curves of anchorless specimens with discontinuous joints under different joint connectivity and rock bridge shapes provided in the embodiments of the present invention;

[0087] Figure 6 This invention provides a comparison of the shear strength of discontinuous joint specimens with different joint connectivity and rock bridge shapes, as shown in the embodiments of the present invention. Specifically, when k = 0.744, τ... p (b) τ when k = 0.744 r (c) τ when k = 0.808 p When (d)k = 0.808, τ r When (e)k = 0.872, τ p When (f)k = 0.872, τ r ;

[0088] Figure 7 A comparison table of test values ​​and theoretical prediction values ​​of rock mass containing non-penetrating structural planes provided for embodiments of the present invention;

[0089] Figure 8 A comparison between the test values ​​of the shear strength of rock mass containing non-penetrating structural planes and the theoretical prediction values ​​of the Lajtai failure criterion provided in the embodiments of the present invention;

[0090] Figure 9 A comparison of the test values ​​of shear strength of rock mass containing non-penetrating structural planes and the theoretical prediction values ​​of the improved Lajtai failure criterion provided in the embodiments of the present invention;

[0091] Figure 10 A flowchart illustrating the method for constructing a shear constitutive model of a discontinuous structural surface provided in an embodiment of the present invention;

[0092] Figure 11 The sliding curve corresponding to the typical discontinuous jointed rock mass shear stress-strain curve provided in the embodiments of the present invention;

[0093] Figure 12 The yield curve corresponding to the typical discontinuous jointed rock mass shear stress-strain curve provided in the embodiments of the present invention;

[0094] Figure 13 The shear-type curve corresponding to the typical discontinuous jointed rock mass shear stress-strain curve provided in the embodiments of the present invention;

[0095] Figure 14 The brittle fracture curve corresponding to the typical discontinuous jointed rock mass shear stress-strain curve provided in the embodiments of the present invention;

[0096] Figure 15 The shear stress-strain curve corresponding to the typical discontinuous jointed rock mass shear stress-strain curve provided in the embodiments of the present invention is a shear composite curve. Detailed Implementation

[0097] To further understand the features, technical means, and specific objectives and functions achieved by the present invention, the present invention will be described in further detail below with reference to the accompanying drawings and specific embodiments.

[0098] Figure 10 This is a flowchart illustrating a method for constructing a shear constitutive model of a discontinuous structural surface according to an embodiment of the present invention, as shown below. Figure 10 As shown, the method for constructing the shear constitutive model of the discontinuous structural surface includes the following steps:

[0099] Step S1: Using different normal stresses σ n Peak intensity τ in the shear stress-strain curve of a discontinuous structural surface at shear failurep and residual strength τ r By fitting the data separately and applying the Mohr-Coulomb criterion, the peak and residual stage shear strength parameters can be obtained: cohesion c and internal friction angle. like Figure 2 As shown;

[0100] The rock shear stress-strain curve typically consists of four stages: elastic stage, pre-peak softening stage, post-peak softening stage, and residual strength stage. Based on the changes in different stages of the curve, the shear stress-strain curves of typical discontinuous jointed rock masses are summarized into five types: sliding type, yielding type, shearing type, brittle fracture type, and shearing composite type, as shown in Table 1. These types are recorded in the literature "Lin Xingchao. Research on the determination method of simulation parameters for failure process of jointed rock mass [D]. Beijing: China Institute of Water Resources and Hydropower Research, 2015." and the literature "Lin Xingchao, Ling Yongyu, Wang Xiaogang, et al. Indoor direct shear test study on jointed rock mass with typical structural plane distribution [J]. Journal of China Institute of Water Resources and Hydropower Research, 2021, 19(01):45-54."

[0101] Table 1 Shear stress-strain curves of typical discontinuous jointed rock masses

[0102]

[0103]

[0104] Step S2: Obtain the rock mass shear strength τ of the discontinuous structural plane in the initial state based on Jennings criterion.

[0105] Specifically, the method in step S2 has the following specific steps:

[0106] Based on the Mohr-Coulomb strength criterion, the shear stress of a discontinuous structural plane is composed of both joint surfaces and rock bridges. That is, the shear strength τ of the rock mass at a discontinuous structural plane is determined by the shear coefficients of the joint surfaces and rock bridges, the cohesion c, and the internal friction angle. Combined with weighted calculation using connectivity k as the coefficient to obtain

[0107]

[0108] in, c is the overall equivalent shear strength coefficient of the structural surface; j , c is the shear coefficient of the joints in the structural plane; r , is the shear resistance coefficient of the rock bridge in the structural plane.

[0109] To characterize the connectivity degree of joints, i.e., the connectivity k, the total length (L) of joint-like structural surfaces is usually used as the unit of measurement. j) or total area (A j ) and the total length of the potential failure slip surface (L) r +L j ) or total area (A r +A j The ratio of 1 / 2 to 1 / 2 is one of the geometric indicators for quantitatively describing rock structure.

[0110]

[0111] Among them, L r A is the total length of the rock bridge structural surface. r This represents the total area of ​​the rock bridge's structural surface.

[0112] Step S3: Introduce the coefficient ξ j and ξ r The normal stress at joints and rock bridges was adjusted separately, and a coefficient ω was introduced to adjust the cohesion of the rock bridges. The shear strength of the rock mass at the adjusted discontinuous structural surfaces was then obtained.

[0113] Wherein, the coefficient ξ j Both ω and ξ take values ​​between 0 and 1, and the coefficient ξ j and ξ r The relationship between the connectivity k between the joints and the joints is as follows:

[0114]

[0115] Step S4, as follows Figure 3 As shown, based on the Lajtai rock bridge failure theory criteria, failure criteria for three discontinuous structural planes—tension, shear, and strength failure—are obtained. The shear strength τ of the rock mass on the discontinuous structural plane is expressed piecewise according to the magnitude of the normal stress, satisfying the following formulas in sequence.

[0116] Criteria for determining tension failure:

[0117]

[0118] Shear failure criterion:

[0119]

[0120] Strength failure criterion:

[0121]

[0122] Where: C is the joint surface adjustment parameter, ranging from 0 to 1; σ t The tensile strength of intact rock, MPa; c r The cohesive force within intact rock, MPa; The internal friction angle of intact rock, in °. The internal friction angle of the intact rock is °.

[0123] Step S5: Obtain the shear constitutive models of the discontinuous structural surfaces corresponding to the tensile failure, shear failure, and strength failure conditions of the rock bridge.

[0124] Specifically, the method in step S5 includes the following steps:

[0125] like Figure 4 As shown, mechanical analysis was performed at different locations on the rock bridge to obtain the normal stress σ of the micro-element. a and tangential stress τ a :

[0126]

[0127] τ a =τ s -kτ j (3-12)

[0128] Where, τ j Characterized as the shear strength of the joint itself.

[0129] Specifically, mechanical analysis of different locations on the rock bridge reveals differences in stress between the ends (points A and C) and the interior (point B). At the ends, the micro-elements are primarily subjected to normal stress (σ). a ) and tangential stress (τ) a The internal elements are affected by the normal stress (σ), while the internal elements are affected by the normal stress (σ). a ) and tangential stress (τ) a In addition to the influence of ), it is also related to the horizontal stress (σ) x )related.

[0130] By analyzing the forces acting on any element on the rock bridge, we can obtain the normal stress σ in the plane at an angle β to the horizontal direction. β and tangential stress τ β :

[0131]

[0132] The normal stress (σ) of the plane β Differentiate with respect to angle β, i.e.:

[0133]

[0134] Substituting equation 3-15 into equations 3-13 and 3-14, we can obtain the maximum and minimum stresses σ1 and σ3 on the principal stress plane:

[0135]

[0136] If the rock bridge experiences initial tensile failure, the minimum principal stress must equal the tensile strength of the rock material, i.e.:

[0137]

[0138] The effective shear stress can be obtained after calculation:

[0139]

[0140] For point A or C at the end of the rock bridge, σ x =0, while at point B inside, σ x >0. Where σ t Since the value is negative, numerically speaking, τ at point A or point C is... a Smaller and relatively easier to achieve initial tensile failure, i.e., the shear stress of the discontinuous structural surface under the condition of tensile failure of the rock bridge is:

[0141]

[0142] Similarly, if the rock bridge experiences initial strength failure, the maximum principal stress must equal the compressive strength of the rock material, i.e.:

[0143]

[0144] The effective shear stress can be obtained after calculation:

[0145]

[0146] For point A or C at the end of the rock bridge, σ x =0, while at point B inside, σ x >0. Where σ c Since it is a positive value, numerically speaking, the value of τ at end point B is... a Smaller and relatively easier to fail due to initial strength, i.e., the shear stress of the discontinuous structural surface under the condition of strength failure of the rock bridge is:

[0147]

[0148] Furthermore, if point B can be considered to be the middle of the rock sample, then the following condition is met. Therefore, equation (3-23) can be expressed as:

[0149]

[0150] Similarly, when a rock sample undergoes shear failure, according to the Coulomb-Navier shear criterion, the effective shear stress... The derivative is shown in Equation 3-14:

[0151]

[0152] achievable In addition, the shear stress τ on the failure surface β and normal stress σ β By conforming to the Mohr-Coulomb strength criterion and substituting equations 3-8 and 3-9 into equation 3-25, the shear stress of the rock bridge at shear failure can be obtained:

[0153]

[0154] For point A or C at the end of the rock bridge, σ x =0, while at point B inside, σ x >0. Where σ c Since it is a positive value, numerically speaking, the value of τ at end point B is... a Smaller and relatively easier to achieve initial shear failure, i.e., the shear stress on the discontinuous structural surface under the condition of shear failure of the rock bridge is:

[0155]

[0156] Thus, the construction method of the shear constitutive model based on discontinuous structural surfaces has been fully determined, and the physical and mechanical meaning of the parameters of this constitutive model is clear. It is applicable to the description of discontinuous structural surfaces with rock bridges. The feasibility of the construction method of the shear constitutive model of discontinuous structural surfaces of the present invention is verified by experimental examples as follows.

[0157] Sample preparation and testing

[0158] Laboratory experiments are one of the most common methods for studying the fracture patterns of rocks, primarily using natural rocks and artificial rock-like structures as research materials. While natural rocks, such as sandstone, granite, and marble, have properties most similar to engineered rock masses, size effects make it difficult to obtain rock samples that both meet experimental dimensions and contain the required complete joint and fracture morphology. Processing techniques such as mechanical drilling, laser engraving, and high-pressure water jetting not only damage the rock samples to some extent but also limit processing precision (apex opening, length, thickness, etc.), and more importantly, cannot produce complex joint and fracture morphologies. Therefore, artificial rock-like structures possess characteristics extremely similar to real rock materials and are easy and inexpensive to manufacture, making them the primary laboratory experimental material for studying complex jointed rock masses. For example, taking the search results of papers published in the authoritative international journal of rock mechanics, *Rock Mechanics and Rock Engineering*, as an example, in the past decade (2013-2023), there were 32 articles with "rock-like" in their titles and 254 articles with "rock-like" in their topics, including 10 ESI highly cited articles. Among the many materials used to create rock-like structures, mortar concrete is simple to produce, has stable properties, is easily ductile, and is inexpensive, making it one of the most common artificial rock-like substrates.

[0159] In this invention, mortar concrete was selected as the experimental substrate. It used 425 white cement (national standard) as the cementitious material, fine quartz sand as aggregate to adjust physical properties such as bonding and friction, and purified water containing 3‰ defoamer as the solvent. The specific ratio of the three components was 100:80:43 by mass. All rock-like samples were thoroughly mixed using an electric mixer, and 140×70×70mm... 3 The samples were solidified in a specially made stainless steel mold for 24 hours, then demolded and cured in clean water for 7 days, and finally cured indoors for more than a month under standard conditions. In addition to the experimental group samples, Ф50×H100 mm samples were also fabricated according to the experimental testing methods recommended by ISRM. 3 Standard cylindrical sample, 70×70×70mm 3 The square sample underwent basic experiments including uniaxial compression, variable angle shear, and Brazilian splitting. The basic mechanical parameters were measured and are shown in Table 2.

[0160] Table 2 Basic physical and mechanical parameters of the tested rock-like substrates

[0161]

[0162]

[0163] All direct shear tests in this invention used the YSZJ-100 rock direct shear apparatus as the loading device. This instrument, manufactured by Chengdu Donghua Zhuoyue Technology Co., Ltd., is a stress-type shear testing device suitable for testing rocks and other related materials. Through microcomputer automatic control, it can effectively control, store, measure, display, and process relevant parameters such as loading time, axial load, axial displacement, horizontal load, and horizontal displacement. In the tests of this invention, the loading method was force loading, with rates of 0.5 kN / s in the normal direction and 0.1 N / s in the horizontal direction.

[0164] Influence of rock bridge morphology

[0165] Figure 5 The results show different joint connectivity (k = 0.744, 0.808, 0.872), different rock bridge shapes (a / b = 0.5, 1.0, 2.0), and different normal stresses (σ). n Shear stress-strain curves of unanchored specimens with discontinuous joints under conditions of 2.5, 5.0, 7.5, and 10.0 MPa were obtained. As the joint connectivity (k) increases, the curves show significant changes, mainly reflected in the shortening of the pre-peak and post-peak softening stages and the decrease in peak intensity (τ). p ) and residual strength (τ) r In terms of the reduction of rock bridge shape (a / b), as the rock bridge shape increases, the rock bridge concentration becomes more concentrated along the shear axis, and the shear failure curves show significant differences. Overall, the post-peak softening stage is prolonged, and the residual strength (τ) decreases under low normal pressure or high joint connectivity. r ) and peak intensity (τ) p The gap decreases; as the normal pressure (σ) decreases... n As the normal pressure increases, the curve changes significantly before and after the peak. At low normal pressure, the curve often drops suddenly when the peak is reached, while at high normal pressure, the curve begins to flatten out and then slowly and smoothly accelerates its decline as the peak approaches. Here, a / b represents the ratio of the lengths in the shear direction.

[0166] As shown in Table 3, in terms of the degree of influence on the shear stress-strain curve type, the unanchored discontinuous joint specimens are most significantly affected by the normal stress, which also conforms to the rule that when the normal force is low, the specimens tend to be brittle fracture or sliding type, and when the normal force is high, the specimens tend to be yielding or shear fracture type. The influence of the rock bridge shape and joint duration is more complex. Generally speaking, it can be considered that as the joint duration increases, the probability of sliding type increases and the probability of brittle fracture type decreases; as the rock bridge shape changes, the closer the length-to-width ratio a / b of the rock bridge is to 1, the greater the probability of brittle fracture type and the smaller the probability of sliding or yielding type.

[0167] Table 3. Influence of rock bridge shape and joint duration on the type of shear stress-strain curve of discontinuous jointed rock mass under anchorless conditions.

[0168]

[0169] Figure 6 The figures represent the rock bridge shapes (a / b) and normal stresses (σ) under different joint connectivity conditions (k = 0.744, 0.808, 0.872). n The peak shear strength and residual strength of the specimens before and after anchoring were compared under the following conditions: (a / b) . It can be observed that as the axial length ratio (a / b) of the elliptical rock bridge along the shear direction increases, the peak shear strength (τ) increases. p All showed varying degrees of decrease. Therefore, the results indicate that the shape of the rock bridge has a significant impact on the shear characteristics of non-connected joints. With the normal stress (σ... n With the increase of τ, the peak shear strength (τ) p The shear peak intensity (τ) increases approximately linearly with increasing joint connectivity (k). p All of them decrease approximately linearly.

[0170] Comparative Analysis of Theoretical Predictions and Experimental Results

[0171] like Figure 7 As shown, substituting each parameter into the calculated theoretical predicted value for each joint connectivity (k) is compared with the peak stress test results of specimens with different rock bridge morphologies, where the adjustment coefficient ξ... j =0.8 and ω=0.9.

[0172] It can be observed that: (a) when the normal pressure is small, the smaller the value of a / b, the larger the peak stress, and the greater the difference with the increase of confining pressure; (b) the original prediction results of the Jennings criterion are all too small under different joint connectivity, rock bridge morphology and normal stress, especially when the normal stress is large; (c) the prediction results of the improved and adjusted Jennings criterion are closer to the experimental results.

[0173] Figure 8 Comparing the calculated values ​​of the Lajtai failure criterion with the experimental results of peak stress in specimens with different rock bridge morphologies, we can find that: (a) the calculated values ​​of both the Lajtai tensile and shear failure criteria are much smaller than the experimental values, with the gap gradually increasing as the normal stress increases and decreasing as joint connectivity increases; (b) the calculated values ​​of the Lajtai strength failure criterion are relatively close to the experimental values, and become even closer as joint connectivity increases. This indicates that the fundamental cause of the final failure of the specimens is strength failure at the rock bridge.

[0174] Figure 9Comparing the calculated values ​​of the improved Lajtai failure criterion with the experimental results of peak stress in specimens with different rock bridge morphologies, we can find that: (a) the calculated results of the improved Lajtai tensile and shear failure criteria are closer to the experimental values. Relatively speaking, the shear failure criterion predicts more accurately when the normal stress is low, while the tensile failure criterion predicts more accurately when the normal stress is high; (b) the calculated results of the improved Lajtai strength failure criterion are slightly closer to the experimental values ​​at low normal stress, but as the normal stress increases, they exceed the experimental values ​​more and more significantly under different joint connectivity conditions. Overall, the improved Lajtai failure criterion is closer to the experimental values, and the fundamental cause of the specimen's final failure, namely tensile and shear failure at the rock bridge, is more consistent with reality.

[0175] The embodiments described above are merely illustrative of several implementations of the present invention, and while the descriptions are specific and detailed, they should not be construed as limiting the scope of the invention. It should be noted that those skilled in the art can make various modifications and improvements without departing from the concept of the present invention, and these modifications and improvements all fall within the scope of protection of the present invention. Therefore, the scope of protection of the present invention should be determined by the appended claims.

Claims

1. A method for constructing a non-continuous structural plane shearing constitutive model, characterized in that, The method comprises the following steps: Step S1, by different normal stresses n The peak strength τ p and the residual strength τ r respectively fitted, according to the Mohr-Coulomb criterion, the peak and residual stage shear strength parameters: cohesion c and internal friction angle Step S2, obtaining the rock mass shear strength τ of an initial discontinuous structural plane based on the Jennings criterion; Step S3, introducing coefficient ξ j and ξ r The normal stress at the joint and rock bridge is adjusted respectively, and the cohesion of the rock bridge is adjusted by introducing coefficient ω, to obtain the adjusted rock mass shear strength τ of the discontinuous structural plane. Step S4, obtaining the failure criterion of three types of discontinuous structural planes, i.e., tension, shear and strength failure, based on the Lajtai rock bridge failure theory criterion; Step S5, obtaining the shear constitutive model of the discontinuous structural plane under the conditions of tension failure, shear failure and strength failure of the rock bridge.

2. The method according to claim 1, wherein The step S2 comprises the following steps: Based on Mohr-Coulomb strength criterion, the shear stress of discontinuous structural plane is composed of joint surface and rock bridge, that is, the rock mass shear strength τ of discontinuous structural plane is composed of shear coefficient of joint surface and rock bridge, cohesion c and internal friction angle The weighted calculation is performed with the connectivity k as a coefficient wherein, is the overall equivalent shear resistance of the structural plane; c j , is the joint shear resistance in the structural plane; c r , is the rock bridge shear resistance in the structural plane.

3. The method according to claim 2, wherein The rock mass shear strength of the discontinuous structural plane in the step S3 satisfies wherein the coefficient ξ j and ω are both between 0 and 1, the coefficient ξ j and the coefficient ξ r are related to the joint connectivity k as follows:

4. The method according to claim 3, wherein The specific steps of the step S4 are as follows: Based on the Lajtai rock bridge failure theory criterion, the failure criterion of three types of discontinuous structural planes, i.e., tension, shear and strength failure, is obtained, and the rock mass shear strength τ of the discontinuous structural plane is expressed in segments according to the numerical size of the normal stress and satisfies the following formulas in turn, Tension failure criterion: Shear failure criterion: Strength failure criterion: Where: C is the joint surface adjustment parameter, 0~1; σ t is the tensile strength of intact rock, MPa; c r is the cohesion of intact rock, MPa; is the internal friction angle of intact rock, °.

5. The method according to claim 4, wherein: The step S5 comprises the following steps: Mechanical analysis is carried out on different positions of rock bridge to obtain micro-unit normal stress σ a and shear stress τ a : where τ j The shear strength of the joint itself is represented by τ s The shear constitutive model of the discontinuous structural plane is represented by τ Obtaining the normal stress σ of the plane at an angle β to the horizontal direction β and the tangential stress τ β : The plane normal stress σ β Differentiating the angle β, i.e.: By substituting formula 3-15 into formulas 3-13 and 3-14, the maximum stress and the minimum stress σ1 and σ3 on the principal stress plane can be obtained: where σ x characterized as a horizontal acting stress; If the initial tension failure of the rock bridge occurs, the minimum principal stress is equal to the tensile strength of the rock material, that is, After calculation, the effective shear stress can be obtained: The shear constitutive model of the discontinuous structural plane under the condition of tension failure of the rock bridge is 6. The method according to claim 4, wherein: The step S5 comprises the following steps: Mechanical analysis is carried out on different positions of rock bridge to obtain micro-unit normal stress σ a and shear stress τ a : τ a = τ s - kτ j (3-12) where τ j characterizes the shear strength of the joint itself, τ s characterizes the shear constitutive model of the discontinuity. Obtaining the normal stress σ of the plane at an angle β to the horizontal direction β and the tangential stress τ β : The plane normal stress σ β Differentiate the angle β, i.e.: By substituting formula 3-15 into formulas 3-13 and 3-14, the maximum stress and the minimum stress σ1 and σ3 on the principal stress plane can be obtained: where σ x characterized as a horizontal acting stress; If the initial strength failure of the rock bridge occurs, the maximum principal stress is equal to the compressive strength of the rock material, that is, After calculation, the effective shear stress can be obtained: The non-continuous structural surface shear constitutive model under the condition of strong damage of rock bridge occurrence is obtained as follows:

7. The method according to claim 4, wherein: The step S5 comprises the following steps: The mechanical analysis is carried out on different positions of the rock bridge to obtain the micro-unit normal stress σ a and shear stress τ a : τ a = τ s - kτ j (3-12) where τ j characterized as the shear strength of the joint itself; Obtaining the normal stress σ of the plane at an angle β to the horizontal direction β and the tangential stress τ β : The plane normal stress σ β Differentiating the angle β, we have: By substituting formula 3-15 into formulas 3-13 and 3-14, the maximum stress and the minimum stress σ1 and σ3 on the principal stress plane can be obtained: where σ x characterized as a horizontal acting stress; When the rock bridge is sheared, according to the Coulomb-Navier shear criterion, the effective shear stress derivation Available In addition, the tangential stress τ β and the plane normal stress σ β According to the Mohr-Coulomb strength criterion, the shear stress of the rock bridge at the time of shear failure can be obtained by substituting Equation 3-8 and Equation 3-9 into Equation 3-25: The shear constitutive model of the discontinuous structural plane under the condition of shear failure of the rock bridge is

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